Statics, equilibrium sphere in a groove on an incline plane

[Nathanael]

Where does F cancel out?

Well right at the beginning you could cancel it out by dividing both sides by F. (Zero divided by F is zero.)

It should cancel at a later step too, but you're making a mistake in one of your steps... You're dividing one side by F but not the other side.

There also seems to be another mistake: you are turning α into θ at the last step. [edit: also the 2 appears to be missing somewhere]

(I haven't read this thread, so I'm just trusting that the initial equation is correct.)

 

[haruspex]

F-(2Fsin(α))/cosθ)=0

That's already wrong. You lost a sin(theta) somewhere.

 

[J-dizzal]

Well right at the beginning you could cancel it out by dividing both sides by F. (Zero divided by F is zero.)

It should cancel at a later step too, but you're making a mistake in one of your steps... You're dividing one side by F but not the other side.

There also seems to be another mistake: you are turning α into θ at the last step. [edit: also the 2 appears to be missing somewhere]

(I haven't read this thread, so I'm just trusting that the initial equation is correct.)

I keep getting the same answer now, still wrong though;

F-(2Fsin(α))/cos(θ))sin(θ)=0
1-(2sinα/cosθ)sinθ=0
cosθ-2sinαsinθ=0
-2sinαsinθ=-cosθ
-2sinα=-cosθ/sinθ
tanθ=1/2sinα
θ=arctan(1/sinα)
θ=50.87 degrees.​

 

[haruspex]

tanθ=1/2sinα
θ=arctan(1/sinα)

Check that step.

 

[J-dizzal]

Check that step.

θ=arctan(1/2sinα)
=50.87 incorrect

 

[haruspex]

θ=arctan(1/2sinα)
=50.87 incorrect

There's another error in the working in the image attached to the OP. Didn't spot it before. You've swapped the 24 degrees and the 66 degrees.

 

[J-dizzal]

There's another error in the working in the image attached to the OP. Didn't spot it before. You've swapped the 24 degrees and the 66 degrees.

yea!
Thanks haruspex.